City have been granted permission to hold talks with the two-time Fifa World Player of the Year after Barca indicated that he is not part of head coach Pep Guardiola's plans.
However, the Eastlands club reportedly face competition from Premier League rivals Chelsea, while Serie A giants Milan have publicly declared their interest in the playmaker.
But Cook is 'optimistic' of luring the Brazil international to City saying, "We are in the hunt and have been talking to them on a regular basis.
"We will continue to do so until we feel it is not right to bring the player to the club or he decides not to come. We know it is a competitive market place.
"There are some complexities (to a possible deal) that you don't normally associate with signing a player.
"Although there is long way to go, we are optimistic. Any great player is welcome here as this is a growth club.
"We are on a journey and are not going to stop until we create a new era."